Hypotheses tests for variance components in some multivariate mixed models

Abstract

Abstract A multivariate mixed model involving exactly one random effect is considered and a locally best invariant (LBI) test is derived for testing the significance of the multivariate variance component corresponding to the random effect. For balanced models, the likelihood ratio test (LRT) is also derived for the same testing problem. In general, the LBI test is different from Pillai's trace test, except for balanced models. The standard multivariate tests based on Wilk's Λ, Pillai's trace and Roy's maximum root are also valid tests for this problem and simulated powers of these tests and the LBI test are reported for several bivariate unbalanced one-way random models. As expected, the LBI test has some advantage over the others for local alternatives. For several bivariate balanced one-way random models, simulation results are also given on the power of the LRT and the tests based on Wilk's Λ, Pillai's trace and Roy's maximum root in order to compare these tests.